Question: Solve for $v$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $-42v+33 < 8v + 91$
Solution: $\begin{aligned}-42v+33 & < 8v + 91 \\\\ -42v&< 8v+58 &(\text{Subtract } 33 \text{ from both sides}) \\\\ -50v &<58 &(\text{Subtract } 8v \text{ from both sides})\\\\ 50v&> -58&(\text{Multiply both sides by }-1)\\\\ v&>-\dfrac{29}{25}&(\text{Divide both sides by }50 \text{ and simplify}) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $v >- \dfrac{29}{25}$.